The following list involves those attractions that are also offered by any tourist guide. This selection gives you some help to orientate yourself in the city, the Hungarian history and culture. The rest is up to your appetite. I also provided some information about each of the attractions without being exhaustive; my only aim was to excite your interest.
The Castle Hill actually involves more than one atrractions. You can find the Castle Theatre, Alexander Palace, Buda Castle Labyrinth museums, galleries and historic monuments there. It is also worth noting that it is a Unesco World Heritage Site.
Castle Hill was settled in the 13th century, when after the Tatar attack citizens realized that there was considerable need for a more easily defensible place to live. The royal Hungarian court also decided to move to the southern end of the hill.
You can approach Castle Hill from Szell Kalman square, either on foot or by bus 16 or 16A. Another option is to walk up, strating your "tour" from the Chain Bridge. Finally you can also take the furnicular (Budavári sikló), which is a bit expensive (~22kn), but quite spectacular.
The following list involves a number of attractions that you can find here:
Royal Palace (in it: National Gallery: http://www.mng.hu; National Széchenyi Library: http://www.oszk.hu;) Perhaps one of the most interesting facts about the Royal Palace that it has never been occupied by the Hungarian Royal family. As far as its style is concerned, it is quite a mishmash. Originally it was built in Gothic style by King Béla IV in the 13th century, however it also signals King Mátyás` (1443-1490) eraly Renaissance taste. Its reconstruction following the Turkish occupation took place in Baroque style.
Mary Magdalene Tower - The only curch that was allowed to remain Christian by the Turkish
Vienna Gate - at the northern end of Castle Hill. It was a marker for non-Jewish merchants in the Middle Ages.
Matthias Church - Similarly to the Royal palace, it is also a mishmash in terms of style with its Gothic, Baroque and Neo-Baroque elements.
Fisherman`s Bastion - Local history says that in the Middle Ages there was a fish market nearby and it was the duty of the fishermen`s guild to defend this part of the castel complex.
The sculpture of a Turul Bird - Turul bird appears in the story of how the Hungarians settled their homeland. It appeared in a dream of the wife of the Hungarian leader Ügyek telling her that she would be the founding mother of a new nation.
Budapest originally was three different cities: Pest (on the eastern side of the Danube), Buda and Óbuda (on the wstern side of the Danube). The three cities were unified only on 17 of November 1873 under the name Budapest. Due to the fact that Budapest is devided by the Danube bridges play an important role in Budapest`s transport.
Chain Bridge - Chain Bridge is the oldest and most beautiful bridge of Budapest. It was built between 1839-1849 at the initiative of Count István Széchenyi after he almost missed his father`s funeral since had not been able to cross the river by ferry due to the bad weather.
Gellert Hill and its surroundings
Gellért Hill is located to the south of Castle Hill; it rises 235 metres above the Danube and offerssome of the most spectacular views of the city. As far as its history is concerned, it was the place where the Venetian bishop Gellért - invited by Saint Stephen to Christianize his people - was killed by the pagans during the great pagan rebellion in 1046. He was rolled down to his death from the hill in a nail-sealed barrel; the hill was named after the martyr.
On the hill among others, you can find the Cave Church, established in 1926 by a Pauline monks. They performed their duties in the Chapel for 17 years (until 1951), when the Communists forced the monks to abandon the temple, arrested them and condemned their superior to death.
Besides Cave Church, Citadella is also worth visiting. It was built by the Hapsburgs in 1848-49 following the War of Independence fought by the Hungarians against them. Basically, it was designed to suppress future rebellions by frightening the population; it did not meet any military requirements.
Last but not least we should not fail to mention the Staue of Liberty among the attractions found on Gellért Hill. This monument is a 14-metre-high statue of a woman, who is pointing to the sky with a palm leaf symbolizing victory. It was erected in 1947 by the Soviet Red Army to pay tribute to their liberation of Budapest from Nazi occupatin, although originally it was designed to the honour of Regent Horthy`s son, who died in the war in a plane crash. However, by the time the statue was finished, Russians were already ruling here - this is how finally the plane propeller was repalced with the palm leaf.
The easiest way to get up to the hill is to take bus 27 from Móricz Zsigmond körtér. You can also walk up enjoying the city views. The best if you start your "tour" from Szent Gellert square; it can be reached either by bus 86, 7E,173E,7, and 173 or by tram 47, 41, 49, 19 and 18.
Memento Park houses a collection of statues that occupied prestigous places in Budapest`s streets during the Communist era. Following the fall of the Communist regime the statues were "relegated" here from the eyes of the citizens. You can reach Memento Park by bus 150. http://www.szoborpark.hu
If you like its exteriror, you should not miss the interior of the Parliamnt although the ticket is quiet expensive (42kn). The most comfortable way to get there is to take tram 2.
Budapest Opera House is among the most beautiful Opera Houses in Europe. If you are an operafun it is good news for you that tickets are available from 13kn. http://www.opera.hu